For x∈R^n define g:R->R by g(t)=f(tx) g'(t)?

[precondition]

Have to use chain rule, so I was thinking,
if we let u(t)=tx where x is the vector,
then g(t)=f(u(t)) so dg(t)/dt=d(f u)(t)/dt=(df(t)/dt)u(t)+f(t)(du(t)/dt)
but then I don't know what to do...

 

[HallsofIvy]

Please state the problme clearly. Is x a constant vector? What is f?

What you have stated is not the chain rule- it looks more like the product rule. f(u(t)) is not "f u".

dg(t)/dt= (df/du)(du/dt).